Question

A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 245 high school seniors in his random sample, 198 believe that getting rich" is an important goal. Can he conclude, at the 0.1 level of significance, that the proportion has indeed changed? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The bull hypothesis a р X The alternative hypothesis: $ The type of test statistic [Choose one) DO OWO D< DO The value of the test statt (round to at least three decimal places) 0 x 5 ? and I The two critical values at the 0.1 level of significance (Round to at least three decimal places) Can we condude that the proportion of high school seniors who believe that getting ridh is an important goal has changed? Yes O NO

Answer 1

Answer:

Ho : p = 0.80

Ha : p != 0.80

sample proportion p^ = x/n = 198/245 = 0.81

test statistic z = (p^ - p)/sqrt(pq/n)

substitute values

= (0.81 - 0.80)/sqrt(0.8*0.2/245)

= 0.39

P value = 0.6965365 [since from z table]

= 0.6965

Here p value > alpha, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.